How does Jerry feel he should act toward his mother?

Jerry feels that he ought to treat his mother with "chivalry," a word that signifies a sort of male code of behavior toward women; it means that Jerry feels an obligation to be loyal to his mother and to honor her with courtesy and generosity.  It is possible that he feels this way because she is a widow, and he is therefore the man in the family, so to speak.  At eleven years old, Jerry is certainly old enough to understand that he is all the family his mother has, and this explains his feeling of "contrition" (which means guilt or remorse) whenever he feels that he has disappointed her.  The narrator even says that Jerry is "very familiar" with his mother's various facial expressions that show her anxiousness, her worry for him, and even her fears about messing up as a parent.  He doesn't want her to feel this way, and so he tries to avoid putting her in this position by treating her with chivalry and thinking of her feelings first.